We report a monocrystalline CdTe/MgCdTe double-heterostructure solar cell with a CuZnS hole contact and ITO electrode. Similar designs have utilized other contact materials in pursuit of high open-circuit voltages and short-circuit current densities--namely, a-Si:H or ZnTe. Cu _x Zn _1-x S is a tunable material system with a low-cost deposition method (chemical bath deposition), which can provide a number of options in terms of bandgap, band offsets, and conductivity. Devices utilizing several different copper compositions, namely x = 15%, 25% and 65%, have been developed and characterized yielding a maximum active-area power conversion efficiency of 12.9%, open-circuit voltage of 956 mV, fill factor of 63.5% and a short-circuit current density of 21.2 mA/cm2. Analysis on the effects of the CuZnS layer on various loss parameters, such as both shunt and series resistance, induced built-in voltages, and parasitic absorption, is also presented.